Of the various types of electrical filter circuits currently used, one of the simplest is a first or second order RC low pass filter circuit. A first order RC network consists of a single resistor and capacitor connected between an input terminal and an output terminal. A second order RC network consists of two such resistors and two such capacitors between the input and output terminals, as specifically illustrated in FIG. 1. This type of low pass filter circuit is highly DC accurate. That is, this type of circuit, which includes no active elements, does not act upon the DC component except to pass it from the input terminal to the output terminal. This is best illustrated in FIG. 2 by means of the solid line curve which graphically illustrates output voltage on the vertical axis as a function of frequency on the horizontal axis for a pure RC filter circuit of the type illustrated in FIG. 1. The DC accuracy of the pure RC filter circuit may be appreciated by noting that in FIG. 2 the DC component (frequency=0) at the output terminal is equal to the DC component at the input terminal.
Although highly DC accurate, it can be seen by reference to FIG. 2 that pure RC filter circuits produce an output voltage which begins to taper off immediately for frequencies above DC, and continues to do so until reaching the cut off frequency F.sub.c. By definition F.sub.c is the frequency at which the input voltage is attenuated by 3 decibels or V.sub.out =V.sub.in .sqroot.2. Ideally, a low pass filter maintains the output voltage equal to the input voltage, i.e., unity gain, throughout a low frequency band between zero frequency and a particular selected cut off frequency, whereupon the input voltage (at and above the cut off frequency) drops to zero. Ideal bandpass filters exhibit a similar instantaneous change between bands of zero and unity gain.
In an attempt to sharpen the roll-off characteristics of filter circuits there have been proposals which combine a pure RC circuit network with circuitry including active components (e.g., operational amplifiers). The active circuit cooperates with the RC network to improve filter performance by reducing pass band roll-off. Unfortunately, such active filters are generally not DC accurate. That is, the output at zero frequency may be equal to the DC component of the input or it may be greater or less than the DC component. This DC offset error typically arises as a consequence of the action of an operational amplifier in attempting to compensate for the presence of the DC component in the input signal.
As is well known, certain implementations of active filter circuits include switched capacitor networks comprised of capacitors, analog switches, and operational amplifiers. As compared with conventional active-RC filters, switched capacitor filters afford the advantage of having filter transfer characteristics determined on the basis of an adjustable clock frequency and capacitor ratios, rather than in accordance with RC products. Since capacitor ratios can be very precisely controlled using existing semiconductor processing techniques, and are stable with temperature, it is possible to achieve very accurate filter transfer functions.
However, in designing active filters incorporating switched capacitor networks it has generally been required to consider the effect of the impedance presented by the resistive and capacitive (RC) elements external to such networks upon the filter response characteristic. Since the filter response characteristic tends to depend upon the clock frequency of the switched capacitor network, when the external or internal clock frequency changes the filter response changes shape. This shape perturbation degrades performance, and in extreme cases may even cause the filter to cease functioning in the desired manner. Therefore, to tune the filter in accordance with the desired response characteristic, external RC elements need to be separately chosen at each clock frequency.